Solid Faces and Normals in Opposite Directions
I think you're misinterpreting what you're seeing.

I don't see any normals displayed in any of the images you've uploaded. When normals are displayed, they look like this:



I might be misunderstanding you. If so, please clarify.

I suspect that the normals are pointing exactly the direction you expect them to point (away from the visible side of the face). If you just Recalculate Normals -> Outside, it should correct the problem.

If that doesn't work, you should check for non-manifold geometry.